Federal Reserve Bank of Minneapolis

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Federal Reserve Bank of MinneapolisResearch Department Staff Report 228Revised March 2003

Hot MoneyV. V. Chari

Federal Reserve Bank of Minneapolisand University of Minnesota

Patrick J. KehoeFederal Reserve Bank of Minneapolis,University of Minnesota,and National Bureau of Economic ResearchABSTRACTRecent empirical work on financial crises documents that crises tend to occur whenmacroeconomicfundamentals are weak, but that even after conditioning on an exhaustive list of fundamentals, asizable random component to crises and associated capital flows remains. We develop a modelof herd

behavior consistent with these observations. Informational frictions together with standard debtdefault problems lead to volatile capital flows resembling hot money and financial crises. Weshowthat repaying debt during difficult times identifies a government as financially resilient, enhancesitsreputation and stabilizes capital flows. Bailing out governments deprives resilient countries ofthisopportunity.Both authors thank the NSF for research support. The views expressed herein are those of the authors

andnot necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

I. Introduction

Financial booms and crises in emerging economies are tightly linked to capital flows:sometimeslarge amounts of capital flowinto a country, leading to a financial boom, and sometimeslarge amounts flow out, leading to a crisis. Two common features of financial crises inemergingeconomies are key to understanding this phenomenon: crises tend to occur in countriesin which macroeconomic fundamentals are weak, and even after the historical crisesdata areconditioned on an extensive list of macroeconomic fundamentals, a sizablenonfundamental,or random, component to the crises remains. (See Kaminsky 1999 and others.)

That random component of international capital flows is the subject of this study.In discussing financial crises, Calvo and Mendoza (1995) argue that a countrys fallfromgrace in world capital markets . . . may be driven by herding behavior not necessarilylinkedto fundamentals. We think the herding story is a promising explanation of the randomcomponent of capital flows that drive financial crises.


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This paper formalizes that herding story. In our model, when macroeconomicfundamentalsare weak, capital tends to flow out. However, weak fundamentals alone do notaccount for all capital flows; herd behavior drives some of them. Investors are uncertainabout whether countries will repay their debt in difficult times. Informational frictions lead

investors to stampede toward or away from a country when the investors have only bitsofinformation. Hence, capital flows in our model have the characteristics of hot money.In our model, we associate financial crises with sudden outflows of capital, as doesCalvo (1998). Our model builds on the work of Banerjee (1992) and Bikhchandani,Hirshleifer,and Welch (1992), who develop stylized models of herdlike behavior in which investorsmustmove in a prespecified order. One contribution of our study is that we endogenize thetimingof investors moves. In our model, investors can invest at any time. They must decide

whetherto make a risky investment in the emerging economy or a safe investment in the rest oftheworld. Information about the riskiness of the investment arrives over time. Specifically,in each period, a signal about the return on the risky investment arrives to the economyand is privately observed by one of the investors. Investors observe the aggregateamount ofinvestment in each period and optimally decide whether to invest or wait for moreinformation.Waiting is costly because of discounting.Our model generates capital flows which are sensitively dependent on the exact patternof signals. If the signals lead investors to be sufficiently optimistic, then investorschoose toforgo the opportunity to acquire information, and they all immediately invest in theemergingeconomy. If investors become sufficiently pessimistic, then they all invest in the rest oftheworld, and capital flows out of the emerging economy. We call such hot moneylikepatternsof capital flows herds.The source of the investment risk in the emerging economy is the possibility ofexpropriationor default by the countrys government. Our model has two types of government: acompetent, or resilient, type, which can efficiently deal with difficult times, and anincompetenttype, which cannot. In the models equilibrium, the competent type never defau lts onits debt while the incompetent type does default, but only during difficult times. Thisfeaturecaptures the idea that in normal times, different types of government may performequally


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well, but difficult times reveal their true nature: some governments crack under pressurewhile others do not.Our model generates the two key features of financial crises documented by Kaminsky(1999). Fundamentals play an important role in generating crises: capital outflows aremore

2likely when fundamentals are weak, and capital inflows are more likely whenfundamentalsare strong. But even when fundamentals are weak, crises cannot be accounted forsolely bymacroeconomic fundamentals. We show that capital flows in or out depending on thespecificpattern of the realization of signals across investors.Our model provides two additional insights. One is that by repaying debt duringdifficult times, governments pass a test of fire and thus enhance their reputation andcapital

flows. Both of those are hurt if governments fail that test. Difficult times are crucial foridentifying financially resilient governments since no such test can occur in normaltimes.The other insight from our model is that bailing out governments in difficult timesinvolves a cost not before appreciated: signal-jamming. Bailouts by outside agents jamsignalsto investors about the governments financial resilience and thus deprive resilientgovernmentsof the opportunity to enhance their reputations. If unanticipated, bailouts dont involvemoralhazard, but they do involve signal-jamming.We interpret our model as suggesting that middle-income countries are most likely toexperience herd behavior. The richest countries have developed institutions to handlecriseswell. Hence, investors do not worry about default in these countries, and a steadystreamof capital flows to them. Similarly, investors have no confidence in the poorest countries ability to handle crises, and essentially no private capital goes to them. Uncertaintyaboutthe resilience of governments is likely to be the highest among the middle-incomecountries,and our model suggests that herd behavior will be most common among them.Our model has many antecedents. Our modeling of the investors builds on elementsof the literature on herd behavior (for example, Banerjee 1992; Bikhchandani,Hirshleifer,and Welch 1992; Caplin and Leahy 1994; and Chamley and Gale 1994). Our modelingof the3government builds on elements of the debt default literature with signaling. (See theEaton


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and Fernandez 1995 survey.)Our work is also complementary to models of financial crises driven by sunspots. (See,for example, Sachs, Tornell, and Velasco 1996; Calvo 1998; Cole and Kehoe 2000; andChangand Velasco 2001.) The sunspot equilibria in these models arise from coordination

problems.For example, in Cole and Kehoe (2000), lending is optimal for an individual lender if andonlyif other lenders are lending. Morris and Shin (2001) critique sunspot equilibria arisingfromcoordination problems. They show that in a large class of coordination games, if agentshavean arbitrarily small amount of idiosyncratic private information about fundamentals,therecan be no (nontrivial) sunspot equilibria. Our model is not driven by coordinationproblems;

nor are our equilibria sunspot equilibria. Thus, our model is not subject to the Morris andShin (2001) critique. Nonetheless, one interpretation of our herding model is that itprovidesa detailed microeconomic story to explain sunspots. In particular, changes in the orderthatsignals are observed can change outcomes dramatically, in much the same way thatsunspotscan change outcomes in models with coordination problems.

II. Macroeconomic Fundamentals and Financial CrisesThe early literature on financial crises, following Krugman (1979), points to themacroeconomic

fundamentals that are likely to play a key role. In this fundamentalist literature, crisescan be completely accounted for by macroeconomic fundamentals. (For some recentworkalong fundamentalist lines, see Atkeson and Ros-Rull 1996 and Burnside,Eichenbaum, andRebelo 2000.)The empirical work on financial crises raises two challenges to the fundamentalist view.4This work shows that fundamentals can account for only a modest fraction of observedcrises.And it shows that even after the historical crisis data are conditioned on an extensive list

ofmacroeconomic fundamentals, a sizable random component remains. (See thereferences inGoldstein, Kaminsky, and Reinhart 2000.)For example, Kaminsky (1999) develops what seems to be an exhaustive list ofindicatorsof financial crises during 197095 for 20 countries, encompassing 102 financial crises.


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The indicators are those suggested by the fundamentalist literature, movements inthings likea countrys output, real interest rates, stock prices, bank deposits, exports, imports,termsof trade, real exchange rate, foreign debt, and M1 money balances. She divides the

sampleperiod into crisis times, defined as the 24 months immediately before an actual financialcrisis,and tranquil times, defined as all other times. Using the crisis indicators, she constructsthe probability that a financial crisis will occur in the next 24 months. She finds that, onaverage, the probability of a currency crisis occurring is .39 in crisis times and .19 intranquiltimes. That is, on average, her fundamentals model mistakenly predicts no crisis 61percentof the time in crisis times and mistakenly predicts a crisis 19 percent of the time intranquil

times.As an illustration, consider Figure 1, which displays Kaminskys (1999) probabilitythat a currency crisis will occur in the next 24 months in Malaysia. Crises actuallyoccurredthere in July 1975 and July 1997. The shaded areas of the graph are the crisis times.Noticethat before the 1975 crisis, the model predicts a relatively low probability of a crisis, butone occurred. In the mid-1980s, the model predicts a high probability of a crisis, butnoneoccurred. In sum, while the data show that fundamentals play an important role infinancialcrises, a very sizable amount of randomness clearly remains.5

III. Investor BehaviorWe build a model which is consistent with those facts. We begin, in this section, bydescribinginvestor behavior during one period of an infinite-horizon dynamic economy, with theriskstructure of investments given exogenously. In the next section, we will build amaximizingmodel of government behavior and provide sufficient conditions for the default decisionsof

this government to generate the risk structure that we assume here.A. Herds with Endogenous TimingConsider one period of a model of a small open economy with domestic and foreigninvestors.The single period has V + 1 stages, denoted t = 0, . . . , V.At each stage, investors must decide whether to make a risky investment in theemergingeconomy or a safe investment in the rest of the world. Information about the returns


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to the risky investment arrives over time in the sense that at each stage a signal aboutthereturn of the risky investment arrives to the economy and is privately observed by one oftheinvestors. Investors observe the aggregate amount of investment at each stage and

optimallydecide whether to invest or to wait for more information. Waiting has both benefits andcosts. The benefit is the possibility of inferring other investors signals from theirdecisions.The cost arises from discounting.The economy has N one-periodlived risk-neutral investors, a fraction of whom are

domestic and a fraction 1 of whom are foreign. (We include domestic investors so

thata failure to make domestic investments corresponds to capital flight.) Each investor has1unit of resources to invest. Investors have a choice of two types of investment: a safe

foreigninvestment with a gross return that is normalized to 1 and a risky domestic investment.The6

payoff on the risky investment depends on the state of the economy, denoted g {G, B},

where G indicates a good state and B, a bad state. The state is realized at stage 0, butis notknown to investors until stage V . The distribution is common knowledge amonginvestors.The common prior probability of the good state at stage 0 is G.

Each investor starts at stage 0 with 1 unit invested in the safe investment and at eachstage t chooses whether to switch from the safe investment to the risky investment.Onceinvestors have switched their unit, they must leave it there until stage V. The riskyinvestmentcompounds at a gross rate R > 0. If the state is good, then the investor gets thecompoundedamount at state V. If the state is bad, then the investor gets the compounded amountwith

probability 0 and gets nothing with probability 1 0. (In the next section, 0 will turn out

to be the probability that the government is competent.) Hence, an investor who

switches atstage t gets a total expected return of

eR(V t){Prt(state is G) + 0Prt(state is B)} (1)

where Prt(state is G) is the conditional probability that the investor assigns to the statebeingG,with similar notation for the state being B. An investor who never switches gets a totalreturn of 1. Notice that after investors switch to the risky investment, they take no more


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actions. Hence, we do not need to define payoffs or strategies for such investors.

Investors receive signals s {G, B} about the state as follows. At each stage t =

0, . . . , S, which satisfies S < V, one signal arrives to the economy and is randomlydistributedto one and only one investor among the set of investors who have not already received

a7signal.1 The signals are informative and symmetric in the sense that

Pr(s = G | g = G) = Pr(s = B | g = B) = > 1/2. (2)

The only publicly observable events are the number of investments at each stage. Letnt denote the number of new investments at t. The public history ht = (n0, n1, . . . , nt1)records the aggregate number of positive investments at each stage up through thebeginningof stage t. Investors also record the signal they receive, if any, and the stage at whichthey

receive it. The history of an investor i at t who receives a signal at stage r is hit = (ht, sr, r),and (ht, , ) denotes the history of an investor who has not received a signal.

Notice that at each stage t, given their histories, investors can be described asbelongingto one of several groups. Any investor who has already invested is inactive. The activeinvestors are of three types: a newly informed investor who has received the signal atthebeginning of stage t, previously informed investors who have received a signal at somestager before t, and uninformed investors who have not yet received a signal.

An investors strategy and beliefs (orpriors) are sequences of functions xt(hit) and

pt(hit) that map the investors histories into actions and priors over the state. The payoffsare defined as follows. Let Vt(hit) denote the payoff for an investor who switches fromthesafe to the risky investment at t conditional on the history hit. ThenVt(hit) = eR(V t)qt(hit)

where for simplicity we let qt(hit) = pt(hit) + 0[1 pt(hit)] is the probability of receiving

1Hence, S investors are randomly drawn without replacement from the pool of N investors and assigned anumber designating the stage at which each will receive a signal. The names of the investors and thestageswhen they will receive the signals are not observed, but the process for assigning names and stages iscommon

knowledge.8the compounded return on the risky asset conditional on the history. Let Wt(hit) denotethepayoff for an investor who waits at stage t. The payoff to waiting is given byWt(hit) =Xhit+1


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t(hit+1|hit)max{Vt+1(hit+1), Wt+1(hit+1)}

where t(hit+1|hit) is the conditional distribution over investor is histories at t+1 given this

investors history at t. Notice that the conditional distribution t(hit+1|hit) is induced from

the strategies and the structure of exogenous uncertainty of the economy in the obvious

way.Notice also that we have imposed symmetry by supposing that all investors who havethesame histories have the same beliefs and take the same actions.Here a perfect Bayesian equilibrium is a set of strategies xt(hit), a set of conditional

distributions t(hit+1|hit), and a set of beliefs pt(hit) such that (i) for every history hit, xt(hit)

is optimal for all active investors, and (ii) the conditional distributions it(hit+1|hit) and the

beliefs pit(hit) are consistent with Bayes rule whereverpossible, but are arbitraryotherwise.To simplify the construction of an equilibrium, we let PG(p) and PB(p) be the posterior

probabilities associated with a good signal and a bad signal, respectively, when theprior isgiven by p. Thus, from Bayes rule we havePG(p) =p

p + (1 p)(1 )

(3)PB(p) =

p(1 )

p(1 ) + (1 p)

(4)

where is defined in (2). Let P (0) = G, P (1) = PG(P (0)), P (2) = PG(P (1)), and so on,

and let P (1) = PB(P (0)), P (2) = PB(P (1)), and so on. Thus, P (k) for k > 0 is theprior probability that the state is good if kgood signals have been received, and P (k) for9k < 0 is the prior probability that the state is good if kbad signals have been received.Notice from the symmetry in (2) that

PG(PB(p)) = PB(PG(p)) = p. (5)It follows from (5) that the effect on the prior of a given set of signals is summarized by

thenumber of good signals minus the number of bad signals in the set. For example,receivingtwo good signals and one bad signal yields the same prior as receiving one good signal.

Let Q(k) = P (k) + 0[1 P (k)]. Notice that Q(k) is an investors belief about the

probability of a risky investment paying off a positive amount, since investors believe thestate is good with probability P (k).Now we consider the region of the parameter space that satisfies these assumptions:


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1 < eR(V S)Q(0) (6)

1 > eRV Q(1) (7)

eRV Q(0) < G(P (0))eR(V 1)Q(1) +B(P (0)). (8)

HereG(p) = P (s = G|p) =p+(1p)(1 ) andB(p)=P (s = B|p) = p(1 )+(1p)

denote the probabilities that the signal is good and bad, respectively, given a prior of p.Note that because R is positive, these assumptions imply the following. Assumption(6) implies that at any stage t, if the investor is forced to choose between the twooptions ofinvesting in the risky investment given belief Q(0) or never investing in the riskyinvestment,investing is better. Assumption (7) implies that at any stage t, if the investor is forced to

choose between the two options of investing in the risky investment given belief Q(1)

or10never investing in the risky investment, not investing is better. We can think ofassumptions(6) and (7) as conditions on the prior P (0).Assumption (8) implies that

eR(V t)Q(0) < G(P (0))eR(V t1)Q(1) +B(P (0)). (9)To gain some intuition for (9), consider an alternative economy in which an investor atstaget expects to receive a signal at stage t +1 with probability 1. Suppose also that theinvestoris restricted to making an investment decision in either stage t or stage t + 1. Inequality(9)implies that in this alternative economy, investing with beliefs Q(0) is dominated bywaitinguntil stage t+1 and investing if and only if a good signal is realized. To understand therole of(8) in our model, note that waiting and receiving information is beneficial becauseinvestorshave the option of not investing if the signals are sufficiently bad. We call this benefit theno investment option value. The cost of waiting comes from a kind of discounting, in thatinvestors forgo the flow return from investing. Assumption (8) requires that the noinvestmentoption value be large relative to discounting. We interpret (8) as an assumption thatinvestorsdiscount the future little.Now we will informally describe the strategies of the various types of investors. At allstages before S, the strategy of the uninformed and previously informed investors is toinvestif and only if the prior is at least P (1). The strategy for newly informed investors is toinvestif and only if the prior is at least P (0). From these strategies, it is easy to construct how


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beliefs evolve.These strategies lead to the following equilibrium outcomes. At the beginning of stage0, one investor receives a signal and is the newly informed investor. That investorinvests if11

the signal is good but otherwise does not. All uninformed investors wait.The decisions at stage 1 depend on the history from stage 0 . If investment was positiveat stage 0, then the uninformed investors infer that the signal at stage 0 was good, theirpriorsrise to P (1), and they all invest, while the newly informed investor at stage 1 investsregardlessof the signal that investor actually received. We say that this history starts a stampedeofinvestment, in that all investors invest regardless of their signals. If investment was zeroatstage 0, then the uninformed investors infer that the signal at stage 0 was bad, their

priorsfall to P (1), and they all wait. The newly informed investor at stage 1 invests if the

signalreceived is good, but waits otherwise.At the beginning of stage 2, if investment has been zero at both stages 0 and 1 ,

then uninformed investors priors fall to P (2), and no investor invests at stage 2 or at

anysubsequent stage. We will say that this history starts a stampede of no investment, inthatall investors do not invest regardless of their signals. If there has been no investment at

stage 0 but an investment at stage 1, then both the uninformed investors and thepreviouslyinformed investor have a prior of P (0), they wait, and the newly informed investorinvests ifand only if the signal is good.More generally, histories of the form (1), (0, 1, 1), . . . , (0, 1, 0, 1, . . . , 0, 1, 1) startstampedesof investment. Histories of the form (0, 0), (0, 1, 0, 0), . . . , (0, 1, 0, 1, . . . , 0, 1, 0, 0) startstampedes of no investment.More formally, we proceed as follows. The strategy for uninformed and previouslyinformed investors isxt(hit) =

1 if pt(hit) P (1)

0 otherwise

(10)


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12

for t S 1 and xS(hiS) = 1 if and only if pS(hiS) P (0). The strategy for newly informed

investors isxt(hit) =

1 if pt(hit) P (0)

0 otherwise

(11)

for t S. Note that p(1) is a cutoff level for investment by the uninformed and previously

informed investors and P (0) is that level for newly informed investors. Note, too, that inorder to invest before S, the uninformed and previously informed investors need to bemore

optimistic than newly informed investors.The beliefs of uninformed investors with history hit = (ht, , ) are recursively defined.

Given pt1(hit1) and a total investment of nt1 at stage t 1, the beliefs at t are given as

follows. For pt1(hit1) equal to either P (1) or P (0),

pt(hit) =

PB(pt1(hit1)) if nt1 = 0PG(pt1(hit1)) if nt1 = 1

P (2) if nt12

(12)where p0(hi0) = G. For pt1(hit1) either greater than or equal to P (1) or less than or equal

to P (2), pt(hit) = pt1(hit1).

The beliefs of the newly informed investors with history hit = (ht, s, t) are simply thoseof the uninformed investors, updated by the newly informed investors signal: pt(ht, s, t) =

Ps(pt(ht, , )) for s = G, B.

The beliefs of the previously informed investor at t who received a signal at t 1 with

history hit = (ht, s, t1) are defined as follows. If no other investor invested at t1, then

this

investors beliefs are the same as they were at stage t 1: pt(ht, s, t) = Ps(pt1(ht1, , ))

for s = G, B. If some other investor invested at t 1, then pt(ht, s, t) = P (2). The beliefs

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of previously informed investors who received their signals before stage t 1 are

recursivelydefined as those of the uninformed investors, except that the recursion now starts at r,withthe beliefs of the newly informed investor at r, pr(hir, s, r).

Built into these beliefs is the idea that investors look at previous investors actions andtry to infer the signals they received. On the equilibrium path and for undetectabledeviationsfrom an investors strategy, the uninformed investors infer the following. If they see oneunitof investment at t and the strategies specify that a newly informed investor receiving agoodsignal should invest, while a newly informed investor receiving a bad signal should notinvest,then the uninformed investors infer that the newly informed investor received a positivesignal.

The uninformed investors update beliefs in a similar way when they see no investmentat t.Notice that when the newly informed investors act differently than their strategiesspecify,these deviations cannot be detected by uninformed investors, so that uninformedinvestorsbeliefs are updated as if the informed investors had not deviated.On the equilibrium path and for undetectable deviations, the newly informed investorssimply update the beliefs of the uninformed investors with their private signals. Thepreviously

informed investor who was newly informed at t 1 simply updates the beliefs of the

newly informed investor at t 1 appropriately. The previously informed investor who

was

newly informed at r < t 1 simply updates the beliefs of the previously informed investor

at

t 1 appropriately.

For detectable deviations, investors infer the following. If an uninformed investor seesmore than one unit of investment, beliefs are updated to an optimistic level, P (2). If anuninformed investor sees other deviations, beliefs are left unchanged. Previouslyinformed

investors behave similarly. A newly informed investor at t who is active at t + 1 and sees14investments by others also updates beliefs to the optimistic level P (2).

These strategies and beliefs induce the conditional distributions t(hit+1|hit) in the

obvious way. We will show that these strategies and beliefs are an equilibrium. Animportant


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feature of the strategies is that the cutoff level for investment is higher for theuninformedinvestors than for the newly informed investors. To understand why this is necessary,supposefirst that both types of investors invest if their beliefs are greater than or equal to P (0).

Tosee why this cannot be an equilibrium, consider a deviation to waiting by an uninformedinvestor at t = 0 with beliefs P (0). Since the newly informed investor invests if and only ifthe investors signal is good, the deviating investor learns the value of the signal. By (8),thisdeviation increases payoffs.Suppose next that the cutoff level for both types of investors is P (1). Suppose the firstsignal is B. Then the newly informed at stage 0 does not invest, and the other investorsinfer

that the newly informed got a bad signal, and their priors are P (1). The newly informed

investor at stage 1 is supposed to wait regardless of the signal. The prior of the

uninformed

investor stays at P (1), and thus, all newly informed investors at all future stages also

wait.After a history of signals B, G, the newly informed investor at stage 1 has a prior of P (0).Adeviation to investing, by (6), raises the payoffs.These arguments help explain why the cutoff levels of the informed and uninformedinvestors must be different. We now show that when these cutoff levels have the form in(10)and (11), the strategies and beliefs are an equilibrium.

Proposition 1. Under assumptions (6)(8), the strategies and beliefs in (10) and(11) constitute a perfect Bayesian equilibrium.15Proof. By construction, the beliefs in (12) satisfy Bayes rule. We repeatedly use theobservation that by construction, for any history hit, pt(hit) = P (k) for some integer k.First consider optimality for histories with no detectable deviations. Consider the

strategies of the uninformed investors with different histories hit. If pt(hit) P (1), then by

(7), waiting is optimal. If pt(hit) = P (0), then by (8), waiting is optimal.More interesting is a history with pt(hit) = P (1). Under the equilibrium, the uninformedinvestor invests and receives eR(V t)Q(1). Suppose the investor instead deviates andwaits. If, for all future histories, the investor ends up investing, then waiting merely

reducesthe length of time in the high return investment, and the investor loses eR at each stage.Thus, the only way that this deviation can be profitable is if there are some futurehistoriesin which this investor never invests. Consider the most pessimistic information theinvestorcould receive. Recall that for such a history, all other active investors invest at t. Thusby


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waiting, the uninformed investor receives no new information from others. By waiting,theuninformed investor could receive a signal in the future. But even if the future signal is s= B,this investors belief will be P (0), and by (6) the investor will invest. Thus, even under

themost pessimistic information, investing is optimal; so waiting is not profitable. Finally, for

histories with pt(hit) P (1), investing is also clearly optimal.

Consider next the strategies of the newly informed investors for some history hit. If

pt(hit) P (1), then (7) implies that waiting is optimal. If pt(hit) P (2), then along the

equilibrium, uninformed investors have already invested, there is no potentialinformation tolearn, and by (6), investing is optimal.The interesting histories are those in which the uninformed investors beliefs are P (0) or

P (1) and the newly informed investor has just received a good signal, so that the

investors16beliefs are P (1) or P (0). The strategy for the newly informed investor specifiesinvesting.Suppose this investor instead deviates and waits, presumably to garner informationaboutthe signals of subsequent informed investors. If for all future histories the investor endsup investing, then for this investor, too, waiting merely reduces the length of time in thehigh return investment. Thus, again, the only way that this deviation can be profitable isifthere are some future histories in which this investor never invests. After such a

deviation, thebeliefs of the newly informed investor are 2 units higher than those of the uninformedinvestorsin that the newly informed investor has beliefs P (k+ 2) when the beliefs of theuninformedinvestors are P (k). The reason is that the newly informed investors private signal raisedthat investors beliefs by 1 unit, and the deviation by the newly informed investor did notaffect that investors own beliefs while it lowered the uninformed investors beliefs by 1unit.

Consider a history hit in which the uninformed investors beliefs are P (1) and the

newly informed investor receives a good signal and, hence, has beliefs P (0). If thenewlyinformed investor deviates and waits, then this deviation triggers a stampede with noinvestment.To see this, note that the deviation causes the uninformed investors beliefs to be

P (2) permanently. Given these beliefs, uninformed investors never invest. Future

newly


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informed investors update their beliefs to at most P (1) and do not invest either. Thus,

this deviation brings the investor no new information. The beliefs of the deviatinginvestorremain at P (0). Assumption (6) then implies that given these beliefs, the optimal actionfor

the newly informed investor is to invest at stage t.Next, consider a history hit in which the uninformed investors beliefs are P (0) and,again, the newly informed investor receives a good signal, so now has beliefs P (1).Supposethe newly informed investor deviates and waits. Then, at the next stage, the uninformed17

investors beliefs fall to P (1) while the informed investors beliefs stay at P (1). Recall

that the deviating investors prior is always 2 units higher than the prior of theuninformedinvestors and that a stampede of no investment starts when the priors of the uninformed

investors reach P (2). Thus, the most pessimistic information that the deviating investorcan get leads to a prior of P (0). At this prior, investing is optimal; thus, the deviation isnotprofitable.Finally, after histories with detectable deviations and at stage S, it is easy to checkthat no investor has an incentive to deviate. Q.E.D.Next we show that within a certain class, the equilibrium we have constructed isunique. We say that a collection of strategies and beliefs is a symmetric, stationaryequilibriumif it is a perfect Bayesian equilibrium and the strategies have the cutoff rule form.Namely,

there are sets of integers I and I0 such that for t S 1 the strategies of the uninformed

and previously informed investors are of the form xt(hit) = 1 if and only if pt(hit) I, while

the strategy for newly informed investors is of the form xt(hit) = 1 if and only if pt(hit) I0.

(Notice that we allow the strategies at S to differ from those at t S 1.) We let the

beliefsbe defined as before.Proposition 2. The strategies and beliefs just described are the unique symmetric,stationary equilibrium.Proof. Consider the investors problem at stage S. Assumptions (6) and (7) imply

that all investors invest if and only if their beliefs are greater than or equal to P (0).Consider

next the investors problem at stage S 1. The newly informed investor can learn nothing

bywaiting, so invests if and only if the investors beliefs are greater than or equal to P (0).Thus,18


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the set I0 is the set of integers with k0. By waiting, an uninformed investor who enters

this stage with beliefs P (0) learns the signal of the newly informed investor. And by (8),waiting is optimal. An uninformed investor who enters this stage with beliefs greaterthan orequal to P (1) will invest at stage S regardless of the newly informed investors action.

Hence,for that investor, waiting only postpones investment, and investing immediately isoptimal.

Thus, the set I is the set of integers with k1. Q.E.D.

B. Public vs. Private SignalsNext we demonstrate that there are two senses in which the capital flows describedabovehave a primary characteristic of hot money; they are excessively volatile. First, we showthat the stampedes in the private signal economy are, in a sense, inefficient relative toan

economy with public signals. Second, we show that the variance of capital flowsconditionalon fundamentals is larger in the private signal economy than in the public signaleconomy.The relevant benchmark here is a public signal economy which captures theinformationallags built into the private signal economy. Consider an economy with informational lagsin which the uninformed investors learn the realization of the stage t signal after theyhavemade their stage t investment decisions. Here, as before, newly informed investorsobserve

the realization of the stage t signal before making their stage t investment decisions.Thus,at t the relevant history of investors is the history of past investments (m0, m1, . . . , mt1)togetherwith the history of the signals. For the newly informed investor, the history of signalsis st = (s0, s1, . . . , st), while that for all other investors is st1. An equilibrium is defined asbefore. For any equilibrium, the outcome path can be defined recursively from thestrategiesand depends only on the history of signals. The equilibrium strategies induce outcomesat19each stage. For the public signal economy, let mt(st) denote the aggregate number ofpositiveinvestments at t for history st. Similarly, in the private signal economy, let nt(st) denotetheaggregate number of positive investments along the equilibrium path at t for history st.We say that the private signal economy has a herd if for some realization of signals st,the economy has a stampede, in the sense that all investors take the same action fromthen


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on, regardless of their signals, and the stampede is inefficient in the sense that theeconomysaggregate investments differ from those of the public signal economy. Formally, theprivatesignal economy has a herd at st if (i) for all future histories sr containing st, nr(sr) is the

same for all sr and (ii) for some future history containing st,PSk

=0 nk(sk) 6=

PSk

=0 mk(sk),

where st skfor all k. We say that the economy has a herd of investment if it has a herd

forsome st andXtk=0

nk(sk) = N

where the summations are over skst. We say that the economy has a herd of no

investmentif it has a herd for some st andXtk=0

nk(sk) < N and nr(sr) = 0 for all sr, r > t, and stsr .

Note that we use the term herd to capture both the idea of a stampede, or cascade, inwhich investors take the same action regardless of their signal (as in Banerjee 1992 andBikhchandani, Hirshleifer, and Welch 1992), and the idea that the actions are inefficientrelative to some benchmark.

Under the following assumption, we show that the private signal economy has herds:eRV Q(1) < G(P (1))eR(V 1)Q(2) +B(P (1))[G(P (0))eR(V 2)Q(1) +B(P (0))].(13)20We think of (13) as a strengthened version of (8), since we know that, given (7), (13)implies(8). Assumption (13) implies that at any t, investing at P (1) is dominated by the followingstrategy: Wait until t+ 1 and at that stage, if the signal is good, invest; if the signal isbad,wait until t + 2, and then invest if and only if the signal is good.Proposition 3. Under (6), (7), and (13), the equilibrium has both herds of investmentand herds of no investment.

Proof. To see that the equilibrium has a herd of investment, consider the history ofsignals of length S, (G, B, B, . . . , B). In the private signal economy, n0 = 1 and n1 = N 1.

In the public signal economy, from (6), (7), and (13), we know that mt = 0 for all t.Clearly,the equilibrium also has herds of no investment. Consider the history of signals of lengthS,

(B, B, G, G, . . . , G). In the private signal economy, nt = 0 for all t, while in the publicsignal


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economy, for S 4 the prior rises above P (0), and investment is positive. Q.E.D.

In (13), we guarantee that in the public signal economy, waiting at P (1) is optimal.Suppose, instead, that we replace (13) with an assumption that guarantees that in thepublicsignal economy, investing at P (1) is optimal. Obviously, the equilibrium outcomes of the

private signal economy are not affected by this change. But now the positive stampedeswould not be herds, because they would coincide with the outcomes of the public signaleconomy.One objection to our definition of herds is that the allocation in the public signaleconomy may be unattainable through an incentive scheme which respects the privacyofsignals. Hence, the public signal economy may not be the right benchmark by which togauge the efficiency of an allocation in the private signal economy. In Chari and Kehoe21(2002), we investigate conditions under which a tax/subsidy scheme which respects theinformational

constraints in the private signal economy can achieve the outcome of the publicsignal economy. The basic idea there is that the private signal economy has aninformationalexternality; each investor weighs the private gains and losses when making aninvestmentdecision but ignores the social gain in information that the investors own actionsprovide.The tax/subsidy scheme varies only with publicly observable events, but helps alignprivateincentives with social incentives.C. Macroeconomic Fundamentals vs. Herds

We turn now to the sense in which international capital flows are driven partly bymacroeconomicfundamentals and partly by herds. We show that our model is consistent withtwo key findings in the empirical work on financial crises. Countries with weakmacroeconomicfundamentals tend to have crises more often than countries with strong macroeconomicfundamentals, and macroeconomic fundamentals alone cannot account for crises.We think of the underlying state of the economy and the prior 0 as capturing themacroeconomic fundamentals. We consider an economy with known fundamentals,what wecall a fundamental economy. The differences in the outcomes in the fundamental and

privatesignal economies result from informational frictions. (We think of the realized signals asmicroeconomic fundamentals which fall below the radar screen ofmacroeconometricians.) Inthe fundamental economy, capital flows are driven by fundamentals: in the good state,fundsflow in with probability 1, and in the bad state, they flow out with probability 1.In the private signal economy, capital flows are driven partly by fundamentals and


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partly by herds. For a prior 0 such that assumptions (6)(8) hold, investments are ofsize N22after histories of the form (1), (0, 1, 1), . . . , (0, 1, . . . , 0, 1, 1). Conditional on the statebeing

G, investments are of size N with probabilitypG = + (1 )2 + (1 )23 + . . . + (1 )N1N =

(1 )N N+1

1 (1 )

(14)where is the probability given in (2). Conditional on the state being B, investments areofsize N with probabilitypB =

(1 ) N(1 )N+1

1 (1 )

. (15)For other histories, investments are between 0 and S/2. If N is large relative to S and thestate is good, then the distribution of capital flows is well-approximated by a binomialwith

realization N with probability pG and 0 with probability 1 pG. If the state is bad, then the

corresponding binomial distribution has probabilities pB and 1 pB.

Capital flows are related to fundamentals. Since pG > pB , capital is more likely toflow in when the state is good and more likely to flow out when the state is bad. Since

both pG and pB are strictly between zero and 1, capital flows are not perfectly correlatedwith fundamentals. Thus, we argue that capital flows are driven partly by fundamentalsandpartly by herds. We summarize this discussion as follows:Proposition 4. Capital flows are related to fundamentals in that pG > pB and aredriven partly by herds in that 0 < pB , pG < 1.In terms of comparing our theoretical model to the empirical literature, we imaginethat the econometrician obtains many realizations of our herding outcomessay, one foreachperiod in the data. For each such period, the econometrician includes enough variablesto pick

up the macro-fundamental, namely, the state g {G, B}, and then computes the

conditional23probability of a financial crisis occurring. This probability is greater when fundamentalsare weak. Nonetheless, even conditioning on the state, the econometrician would find anontrivial residual (conditional) variance. If, instead, the outcomes were obtained fromthe


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fundamental economy, then the correlation between crises and fundamentals would beperfect,and the econometrician would find a zero conditional variance. This is the sense inwhich ourmodel is consistent with the empirical work mentioned above.

D. Other Regions and Nonstationary EquilibriaSo far, we have focused on what we consider to be the most interesting region of theparameterspace. Now we briefly discuss the characteristics of symmetric, stationary equilibria forotherregions.If the rate of return R is so low that eRV Q(1) < 1, then investors never invest regardless

of the signals. If the rate of return R is so high that eR(V S)Q(1) > 1, then all investors

investat stage 0. If R is lower than what we have, but satisfies eRV Q(0) < 1, yet eR(V S)Q(1) > 1,then the equilibrium is very similar to the equilibrium described above. Specifically, the

aboveequilibrium needs one good signal to set off a positive herd and two bad signals to setoff anegative herd, while this one needs two good signals for a positive herd and one badsignalfor a negative herd.Next, if parameters are such that the value of waiting at P (0) is less than the value ofimmediately investing (if the direction of the inequality is reversed in the analog of (8),wherethe right side is now the payoff to the optimal strategy following waiting), then allinvestors

invest at stage 0.Finally, we have focused on a region of the parameter space such that, except for the24last stage, the equilibria are stationary, in that they depend only on the prior and not ontime.

If we assume instead, for example, that (7) is replaced by eRV Q(1) > 1 > eR(V S)Q(1),

then the equilibria are necessarily nonstationary and will depend on time as well as theprior.We have also focused attention on a stationary equilibrium. Under assumptions (6)(13), the economy also has nonstationary equilibria. For example, consider thestrategieswe have proposed with the single change that the newly informed investor at stage 0waitsregardless of the signal. Then, at stage 1, the beliefs of the uninformed investors stay atP (0)regardless of the action of the newly informed investor at stage 0. To show that this isan


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equilibrium, we need only show that the newly informed investor prefers to wait whenthe signalis good. By (13), waiting is optimal. It is easy to show that the qualitative characteristicsof these nonstationary equilibria are the same as those of the stationary equilibrium.

IV. Endogenous Government Behavior

So far we have worked out the behavior of the investors in our model assuming aparticularset of returns for the risky investment. Now we explicitly model the source of risk asarisingfrom default or expropriation decisions by governments.We construct a simple maximizing model of government behavior. In our model, thegovernment can be either competent or incompetent. Both types of government doequally wellat governing during normal times, but a competent government is better than anincompetentone at dealing with difficult times. Normal times correspond to the state being good

whiledifficult times correspond to the state being bad. Investors initially do not know the typeofthe government, but have prior beliefs 0 that the government is competent.After we set up this version of the model, we provide sufficient conditions for the25competent government to never default on what it owes and for the incompetentgovernmentto default only in difficult times. Under these conditions, the return on the riskyinvestmentis given by (1), as in the model without government. We then derive two new insights

fromthis model with government.A. The Dynamic EconomyThe dynamic economy is as follows. The economy has an infinite number of periods,each ofwhich is divided into V +1 stages. The timing and information structure within eachperiodare as before. The investors live one period and, hence, face the same problem asbefore. Theinteresting agent now is the government, which takes actions on behalf of domesticworkers.

The state of the economy, g, follows an exogenously given i.i.d. process over normaltimes with probability G and difficult times with probability B (= 1G). The government

must provide more services in difficult times than in normal times. We denote the levelofgovernment services in normal times by G and that in difficult times by B. Thegovernmentmust finance spending on these services with a combination of taxes on investment and


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distorting domestic taxes. In each period, the tax rates on investment {0, 1}, so that

= 1 corresponds to default. Tax revenue consists of revenue from domestic taxes Tplus

revenue from taxes on investment x, where the level of investment x {0, 1, . . . , N}.

During normal times, both types of government can govern equally well, but duringdifficult times, the types differ in how efficiently they can transform tax revenue T + xintogovernment services. (For a related setup, see Rogoff and Sibert 1988.) Since bothtypesof government are equally efficient in normal times, for simplicity we normalize the levelofgovernment services that need to be provided in normal times to be G = 0. Duringdifficult26times, however, both types need to provide a level of services equal to B. We assume

thata government of type i = C, I (for competent and incompetent) provides 1 unit ofservicesfor every i unit of revenue it receives. We normalize C = 1 and assume that I > 1; isthus an incompetency parameter. In this sense, our model captures the idea that onlyduringdifficult times do the major differences between the two types of governmentmaterialize.During difficult times, the governments budget constraint is iB = T + x. Duringnormal times, when G = 0, tax revenue is distributed as lump-sum subsidies to workers.We capture the distortions associated with domestic taxes by letting output be a

decreasingfunction of domestic tax revenue T, denoted y(T ) as long as T is positive and y(T) = y(0)otherwise. An investment of size x generates extra income of wx for the domesticworkers,where w is the labor income generated by each unit of investment. This extra incomerepresentsthe benefits to the country of having investment. The consumption of domestic workers

is given by c = y(T) +wx T . The period utility function of the government is linear in the

consumption of domestic workers. For algebraic simplicity, we assume that thegovernmentdoes not care about the consumption of domestic investors. From the budget

constraints ofthe government and the workers, it follows that the period utility of government iexpressedas a function of the level of government services g, the investment level x, and thedefaultdecision is given by

U i(g, x, ) = y(ig x) + wx (ig x).


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The government discounts future utility at rate .The timing of events within a period is as follows. First, the investors receive signalsabout the state of the economy and make investment decisions in S stages as describedabove.27

Second, at stage V the government provides some level of services, and it is publiclyrevealedwhether times are normal or difficult. Third, the government makes its taxation anddefaultdecisions. And finally, private investors consume.We assume that the governments default decision is publicly revealed, but thatinvestorsdo not observe domestic tax revenue. (This last assumption prevents the investorsfrom inferring the governments type in difficult times, from its budget constraint.) For an analysis of the governments decision problem, the relevant aspect of theinvestors

decisions is the probability of investing conditional on the realization of g {G, B}given the investors priors . Our equilibrium has only three relevant priors: the initialprior0 and priors of 0 and 1. This is because in our equilibrium, either the types pool, andtheprior stays at 0, or they separate, and the prior moves to 0 or 1.We let pG(x; ) and pB(x; ) denote the probability of an investment of size x when theprior is and the state is G and B, respectively. Constructing these probabilities is easy,giventhe behavior of investors we have described in the previous section. For example, pG(N ;0)

is given by pG in (14), while pB(N; 0) is given by pB in (15). To compute, for example,pG(1; 0) and pB(1; 0), note that an investment of 1 unit occurs when the signalrealization

begins with (B, G, B, B). Thus, pG(1; 0) = (1 )(1 )2 and pB(1; 0) = (1 )2.

When = 1, it follows from the definition of Q(k) that Q(k) = 1 for all k, and funds ofsize N flow in with probability 1. Hence, pG(N; 1) = pB(N; 1) = 1. When = 0, both typesdefault in our equilibrium, and funds never flow in. Hence, pG(0; 0) = pB(0; 0) = 1.We focus on a Markov equilibrium in which government strategies and investor updatingrules depend only on the state variables , g, and x. The government takes as given28

the investing probabilities pG

(x;) and p

B

(x;) and chooses the default decision

tosolve

W i(, g, x) = max

U i(g, x, ) + Xg0=G,B

g0XN


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x0=0

pg0(x0; 0)W i(0, g0, x0)where 0 = (, g, x, ) is the updating rule for the beliefs about the type of governmentand W i(, g, x) is the value function for government i. Clearly, if x = 0, there is no defaultdecision. This dynamic programming problem gives decision rules of the form i(, g, x).A perfect Bayesian equilibrium consists of default rules for the competent andincompetent

types of government, C() and I(); an updating rule () for the prior; and the

probability of investing rules pG() and pB(), such that (i) given the updating and

investingrules, the default rules solve the governments dynamic programming problem; ( ii) theprobabilityof investing rules are consistent with the optimality of investors decisions given theirbeliefs; and (iii) the updating rule satisfies Bayes rule whenever possible.We focus on an equilibrium in which the two types of government pool in normaltimes and separate in difficult times. More precisely, we focus on equilibria in which if

= 0or 1, in normal times neither type of government defaults, while in difficult times only theincompetent type defaults. If = 0, there is no investment in equilibrium. Off theequilibriumpath, if there is investing, both types default. In our construction of an equilibrium, wedefinestrategies and updating rules only at the initial prior 0, together with priors of 0 and 1.Whiledefining strategies and updating rules for all priors is straightforward, none of the otherpriorscan be reached regardless of the behavior of the investors or the government.

Formally, when x 1, the strategies are C(, g, x) = 0 if {0, 1} and g {G, B}

and C(, g, x) = 1 otherwise, while I(, g, x) = 0 if {0, 1} and g = G and I(, g, x) =

1 otherwise. For x = 0, there is no default decision. The updating rule for beliefs (, g,x, )29

is, for x 1,

(, g, x, ) =

0 if = 11 if = 0 and g = B if = 0 and g = G

(16)and, trivially, for x = 0, (, g, 0, ) = , for all g.Along the equilibrium path, the behavior is as follows. Starting from the initial prior


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and any investment x 1, the two types of government pool by repaying in normal

times,and the prior is unaffected. When difficult times come, the types separate: thecompetentgovernment repays, and the incompetent government defaults. The priors move to 1

and 0,respectively. After this separation, investors invest with probability 1 with the competentgovernment in all future periods, and this government never defaults. Investors neveragaininvest with the incompetent government.2For these conjectured strategies and beliefs to constitute an equilibrium, certaininequalitiesmust hold. We will develop these inequalities and show that they hold under thefollowing three assumptions:

y(B N) + N y(B)

wN1 y(B 1) y(B) + 1

B

1

(17)

where = [y(B N) + N ] [y(B 1) + 1];

w x

1 N (18)

2Clearly, we can extend the model to have a more complicated pattern of signaling than that consideredhere. By adding more government types and various states, we could have equilibria in which in less

severecrises, only the most incompetent types default and hence separate, while in the more severe crises, allbut themost competent types default and separate. We could also allow government types to evolvestochasticallyover time, say, by letting them follow a Markov process (as in Cole, Dow, and English 1995). With such aspecification, after a sufficiently long period has passed after a default, lending restarts as the types driftbackin expectation to the mean. Under either of these extensions, our main results would go through, andwhilethe pattern of signaling would be richer, the algebra would become significantly more complicated.

30where x = GPN

x=0 pG(x; 0)x + BPN

x=0 pB(x; 0)x is the expected level of investment xgiven a prior 0; andw

1


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XNx=0

pB(x; 0)x N [1 pB(0; 0)]. (19)

To interpret (17), suppose that the function y is concave as well as decreasing. Then, ifN were equal to 1, the expression on the left side of the first inequality sign would

necessarilybe less than the expression on the right side of the second inequality sign. Assumption(17)is more likely to be satisfied, then, the more concave is the function y, the larger is theincompetency parameter , and the smaller is N. Concavity of y is a natural assumptionand follows if the marginal deadweight cost of taxation is increasing in tax revenues, asistypically assumed. Assumption (18) requires that the present value from next period onofthe average extra benefits from investment is greater than the onetime gain in reducedtaxes

from defaulting. Notice that both (18) and (19) are more likely to be satisfied the larger is. We prove the following proposition in the Appendix:Proposition 5. Under (17)(19), the constructed strategies and beliefs constitute aperfect Bayesian equilibrium.B. Two InsightsThis model with government provides two new insights about financial crises inemergingeconomies.B.1. The Necessity of Difficult Times for Signaling: Tests of FireOur model is predicated on the idea that difficult times provide an opportunity for acompetent

government to signal its competency by taking actions which are too costly for an31incompetent government to mimic. Thus, we argue that difficult times act as tests of firethat determine the true nature of a government. But is there some other way for thegovernmentto signal its competencysay, by taking some costly action in normal timeswhichwould work just as well? We say no, because in normal times, whatever a competentgovernmentwould like to do to separate itself, an incompetent government would like to do atleast as muchand can. If the competent government tried to separate itself by takingsome

action, then the incompetent government would mimic this action and destroy thesignalingcontent of the action. Therefore, for a true separating test, difficult times are needed.Consider a candidate test in normal times. Suppose an equilibrium exists in whichthe competent government takes a costly action during normal times to signal that it iscompetent. This action could be interpreted in many ways. It could be thought of, forexample, as some domestic reform that is costly but might be seen as a show of goodfaith.


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For simplicity, here we simply let governments pay money to foreigners to try to signaltheircompetency. We will show by way of contradiction that such payments could not serveasa separating signal. The potential for other costly actions, like reforms, to serve as a

signalcould be analyzed in a similar way.For concreteness, suppose a signaling payment z is made to some foreign entity whichproves to investors that the government is competent. If this payment successfullysignalsthe governments type, then the competent government will have an incentive to makethepayment while the incompetent government will not. If that is so, then for a governmentstarting in normal times with a prior of 0, making the payment causes the prior to moveto1, while not making it causes the prior to move to 0 .

32Proposition 6. Under (17), a government cannot make payments to signal itscompetencyin normal times.The idea of the proof of this proposition, given in the Appendix, is straightforward.For the two types of government, the current-period payoffs are the same. For futurepayoffs,however, the incompetent type values a change in the prior from 0 to 1 more than thecompetent type does. In the future, the competent type gains only the extra benefits oftheinvestment project. The incompetent type could mimic the competent type and gain only

these extra benefits, too, but here, as in the equilibrium without a signaling payment, theincompetent type gains more by defaulting in the bad state. Thus, whatever thecompetentgovernment would pay to signal its type, the incompetent would also pay, and suchpaymentscannot serve as a separating signal.B.2. The Cost of Bailouts: Signal-JammingOur model provides another insight as well, this one about the effects on equilibriumoutcomesof outside agencies bailing out governments apparently about to default on debt. Weshowthat such bailouts in difficult times can interfere with the signaling processbailouts jamthesignals to investors about the type of government they have invested in. Thus, whilebailoutsmay have short-term benefits, they impose long-term costs on the government beingbailedout. We argue that these signal-jamming costs can arise even if a bailout isunanticipated.


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To make these benefits and costs concrete, suppose that an economy is in difficulttimes, the state has been revealed, and the government is on the verge of defaulting onitsdebt. Suppose that an outside agency undertakes a onetime unanticipated bailout bymaking

a gift of goods to the government equal to the size of the investment x, earmarked forrepaying33investors for their claims.This bailout clearly has short-term benefits: with it, both types of government canreduce their distortionary taxes in difficult times by x. For the incompetent government,the bailout also has long-term benefits: without it, this type of government would revealitstype by defaulting, while with the bailout, it can conceal its type by not defaulting. Forthe competent government, however, the bailout has long-term costs: in effect, thebailout

jams the competent governments signal of competency. Without the bailout, this type ofgovernment would reveal its type by repaying, while with the bailout, it is deprived of theopportunity to do that.The competent government thus faces a trade-off between the bailouts short-termbenefits of tax reduction and the bailouts long-term costs of signal-jamming. For thisgovernment,the value of utility under a bailout of size x when an investment of size x has

been made is y(B x) + wx (B x) + V C(0) since the government is able to reduce

its distorting taxes by x but investors priors stay at 0. Here V C() denotes thecontinuationutility of a competent government with a prior of . The utility without a bailout is

y(B) + wx B + V C(1). Thus, the government has higher tax rates in the current period,

but investors priors move to 1. The short-term benefits

y(B x) y(B) + x (20)

arise because the government needs to raise less tax revenue, which has the directeffectof raising consumption by x, and the indirect effect of allowing the government to lower

distortions and, thus, raise output. The long-term costs are [V C(1) V C(0)]. These

costsarise because the bailout interferes with the market mechanism that allows the

competent34government to signal its type and raise its prior from 0 to 1. By jamming that signal,thesebailouts lead the competent government to remain in the region with herds and volatilecapital flows instead of moving to a region with no herds and smooth capital flows. Onlywhen the next difficult times occur is the government able to signal its type. Using t (26)and (30) from the Appendix, we can derive that these costs are equal to


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w(N x)

1

h

1 B

PN

x=1 pB(x; 0)i. (21)In sum:Proposition 7. Bailouts of governments have short-term benefits, but even ifunanticipated,they have long-term costs.The point of Proposition 7 is that while bailouts may well benefit both types ofgovernment,they also impose costs. In the literature, most attention has been focused on the moralhazard costs of bailouts, and these costs are now well understood. If bailouts are

unanticipated,they do not lead to moral hazard. We show that even unanticipated bailouts imposeanother type of cost, arising from signal-jamming, one which has not received attention.So far we have assumed that governments have no choice on whether to accept orreject a bailout. It is easy to show that if (20) is larger than (21), then both types willacceptthe bailout and that such an inequality is not inconsistent with our other assumptions.

V. ConclusionHere we have constructed a simple model of how informational frictions in internationalfinancial markets and standard debt default problems produce herdlike capital flows withthe

characteristics of hot money. We have shown that our model can qualitatively accountfor the35findings of Kaminsky (1999), that financial crises in emerging economies involve bothweakfundamentals and a random component. Further research should assess whether aversion ofthe model can quantitatively account for Kaminskys findings.For simplicity, we have assumed here that investment is a zero/one decision and thatinvestors have no means to communicate their signals. In recent work, Chari and Kehoe(2002), we show that herds also arise in models with continuous investment and

communication.36Appendix: Proofs of Propositions 5 and 6Proposition 5. Under (17)(19), the constructed strategies and beliefs constitute aperfectBayesian equilibrium.Proof. We begin to prove Proposition 5 by analyzing the behavior of a competentgovernment.


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In difficult times, with a prior of 0 or 1 and any investment level x, a competentgovernment is supposed to repay its debt to investors and get a new prior of 1 ratherthandefault and get a new prior of 0. For that assumption to be true, the following must holdfor

all x:y(B) + wx B + V C(1) y(B x) + wx (B x) + V C(0). (22)

That can be rearranged as

[V C(1) V C(0)] y(B x) y(B) + x. (23)

Here V C(1) and V C(0) are continuation payoffs to the competent governmentassociated withpriors of 1 and 0, respectively. These continuation payoffs are the present value ofexpecteddiscounted utilities from the next period on under the equilibrium strategies. We willshow

that for an investment of size N ,[V C(1) V C(0)] =

wN

1

. (24)Then, from (17) and (24), (23) follows. In particular, we conclude thatwN

1 y(B N) + N y(B). (25)

37In (25), the left side of the inequality is the discounted sum of benefits the competent

governmentloses by having the prior move from 1 to 0 , while the right side of the inequality isthe current gain the government gets by defaulting today on the investment.To see this, note that with a prior of 1 , funds always flow in, and the competentgovernment never defaults, so its continuation payoff is given by

V C(1) = G[y(0) + wN] + B [y(B) + wN B] + V C(1). (26)

With a prior of 0, funds never flow in, and the continuation payoff is given by

V C(0) = G[y(0)] + B [y(B) B] + V C(0). (27)

Subtracting (27) from (??), rearranging terms, and multiplying by gives (24).Now consider the competent government in normal times with a prior of 0. For this

government to repay at 0 and continue with this prior rather than default and have anewprior of 0, this must hold for all x:

y(0) + wx + V C(0) y(0) + wx + x + V C(0) (28)

which it will if it holds for x = N. Thus, we need only show that

[V C(0) V C(0)] N. (29)

The continuation payoff V C(0) is implicitly defined by


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V C(0) = GXNx=0

pG(x; 0)[y(0) + wx + V C(0)] (30)

+BpB(0; 0)[y(B) B + V C(0)]

+BXNx=1

pB(x; 0)[y(B) + wx B + V C(1)].

38To understand (30), recall that with probability B pB(x; 0), difficult times occur, and the

government receives funds of level x from investors. If x 1, then the competent

governmentrepays the investors and gets a new prior of 1 (while the incompetent government in thecorrespondingstate defaults). In the other events, no information is revealed: The governmentreceives the current payoff under the equilibrium strategy for that event and acontinuationpayoff V C(0).To establish (29), note first that since the continuation payoffs are increasing in the

prior, V C(1) V C(0). Using this inequality in (30) and rearranging gives

V C(0) G[y(0)] + B [y(B) B] + w x + V C(0). (31)

Subtracting (27) from (31) and rearranging terms gives

V C(0) V C(0)

w x

1 . (32)Together, then, (32) and (18) imply (29).In normal times with a prior of 1, the competent government has a similar inequality.Since the continuation payoff is increasing in the prior, this inequality is automaticallysatisfied whenever (29) holds.Next we analyze the behavior of an incompetent government. In difficult times with aprior of either 0 or 1, this type of government is supposed to default on its debt andhave anew prior of 0 rather than repay and have a new prior of 1. For that assumption to betrue,

this must be true for all x:

y(B x) + wx (B x) + V I(0) y(B) + wx B + V I(1). (33)

For (33) to hold, a rearranged version of (33) must hold for x = 1:

y(B 1) y(B) + 1 [V I(1) V I(0)]. (34)

39Here V I(0) and V I(1) are continuation payoffs for the incompetent governmentassociated


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with priors of 0 and 1, respectively. With a prior of 0, funds never flow in, and thecontinuationpayoff is given by

V I(0) = G[y(0)] + B[y(B) B] + V I(0). (35)

With a prior of 1, funds of size N flow in today. Tomorrow, under the equilibrium

strategies,the incompetent government repays and keeps the prior of 1 in normal times, while itdefaultsand gets a new prior of 0 in difficult times. Hence, the continuation payoffs are

V I(1) = G[y(0) + wN + V I(1)] + B[y(B N) + wN (B N) + V I(0)]. (36)

Subtracting (35) from (36) and rearranging terms gives

V I(1) V I(0) =

wN + B[y(B N) y(B) + N ]

1 G

. (37)Using (37) in (34), we need only show that

(1 G)[y(B 1) y(B) + 1] {wN + B [y(B N) y(B) + N ]} . (38)

Recall that we have defined = [y(B N) + N] [y(B 1) + 1] . Using that, we can

reduce (38) to

y(B 1) y(B) + 1

1

[wN + B]. (39)

Hence, (34) follows from (17).Next, in normal times, the incompetent government is supposed to repay its debt withpriors of 0 and 1. Clearly, if the government repays with a prior of 0, it will repay with aprior of 1; hence, we need only consider a prior of 0. Under this prior, the government is40supposed to repay and keep the prior 0 rather than default and get a new prior of 0 .Hence,we must have that

y(0) + wx + V I(0) y(0) + wx + x + V I(0) (40)

for all x, which is equivalent to

[V I(0) V I(0)] N. (41)The continuation payoff under 0 is given byV I(0) = GXNx=0

pG(x; 0)[y(0) + wx + V I(0)]

+ B pB(0; 0)[y(B) B + V I(0)]

+B


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XNx=1

pB(x; 0)[y(B x) + wx (B x) + V I(0)].

To understand this payoff, note that tomorrow, with probability BPN

x=1 pB(x; 0),the government receives funds in difficult times and defaults, and its prior falls to 0. Intheother events, the government does not default, no information is revealed, and thegovernmentcontinues with the original prior 0. Subtracting V I(0) in (35) from V I(0) above gives

(1 {1 B[1 pB(0; 0)]})[V I(0) V I(0)] (42)= w x + BXNx=1

pB(x; 0)[y(B x) y(B) + x].

Now the right-most inequality in (17) implies that

y(B x) y(B) + x

wx

1

(43)41and (18) implies that

w x

1

N. (44)Using (43) and (44) in (42) gives that the right side of (42) is greater than or equal to

1

N +Bw

1

XNx=1

pB(x; 0)x. (45)We can use this relation and (42) to imply that a sufficient condition for (41) is that"

1

N +Bw


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1

XNx=1

pB(x; 0)x#

(

1

"

1 B

XNx=1

pB(x; 0)#)

N

which, with some manipulation, reduces tow

1

NPN

x=1 pB(x; 0)PN

x=0 pB(x; 0)xwhich is implied by (19). Q.E.D.Proposition 6. Under (17), a government cannot make payments to signal itscompetency

in normal times.Proof. By way of contradiction of Proposition 6, suppose that such a signalingequilibriumexists. In particular, suppose that a payment of z successfully signals the competentgovernments type in normal times when there has been an investment of x. Then thecompetentgovernment must prefer to make the payment and have a prior of 1 rather than notmake the payment and have a prior of 0. Thus,

y(z) + wx z + V C(1) y(0) + wx + V C(0). (46)

Moreover, an incompetent government must prefer to not make the payment signalingcompetency,so that

y(z) + wx z + V I(1) y(0) + wx + V I(0). (47)

42To show that (46) and (47) cannot hold, we need only show that

V C(1) V C(0) < V I(1) V I(0). (48)


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If such a signaling equilibrium existed, an incompetent government would have anincentiveto deviate and actually make the payment. Using (??) and (37), we can write (48) aswN

1

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Federal Reserve Bank of Minneapolis